Details

sample18.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	98×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series25.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	460	585
1	1938	554
2	5002	551

prune123.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	3	71

Merged error: 0b

Counts

71 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
232×	`sqrt-prod`
192×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 317

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
20.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
15.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
34.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify132.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1126	5982
1	4661	5345
2	5002	5337

prune579.0ms

Filtered

147 candidates to 329 candidates (-123.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	329	3	332

Merged error: 0b

Counts

332 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
27.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify97.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	856	1494
1	4169	1377
2	5002	1353

prune203.0ms

Filtered

94 candidates to 144 candidates (-53.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	144	3	147

Merged error: 0b

Counts

147 → 3

regimes62.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample459.0ms

Algorithm

intervals

Results

221.0ms	7995×	body	80	valid
69.0ms	2668×	body	80	nan
1.0ms	5×	body	1280	valid

Details

sample18.0ms

simplify3.0ms

prune7.0ms

localize5.0ms

rewrite16.0ms

series25.0ms

simplify48.0ms

prune123.0ms

localize9.0ms

rewrite56.0ms

series70.0ms

simplify132.0ms

prune579.0ms

localize8.0ms

rewrite39.0ms

series51.0ms

simplify97.0ms

prune203.0ms

regimes62.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample459.0ms

Profiling